**CUNEF**

Practice III - Retail score analysis

Machine Learning</strong>

Pablo Mazariegos Reviriego - pablo.mazariegos@cunef.edu

Mario Sabater Pascual - mario.sabater@cunef.edu

In this Machine Learning practice we will be working with the Yelp dataset. The whole practice will be composed by the following notebooks:

1. Data Reading and Problem statement
2. Data selection & variables preparation
3. EDA
4. Model selection
5. Best Model and Explainability
6. **Variables Relationship (Graphs)**

Creating Graphs

Graphs are networks consisting of nodes connected by edges or arcs. In directed graphs, the connections between nodes have a direction, and are called arcs; in undirected graphs, the connections have no direction and are called edges

• Libraries import and dataset load
• Variables Relationship (Graphs)

**Libraries import and dataset load**

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import matplotlib.cm as cm
import networkx as nx
import warnings
warnings.filterwarnings('ignore')

Data Read

pd.set_option('display.max_columns', 500)
restaurants = pd.read_csv('../data/processed/restaurants_models.csv')
restaurants.head(3)

	stars	review_count	is_open	restaurants	food	bars	sandwiches	american (traditional)	pizza	coffee & tea	breakfast & brunch	american (new)	fast food	burgers	mexican	italian	specialty food	seafood	desserts	bakeries	salad	chinese	cafes	chicken wings	ice cream & frozen yogurt	beer	sports bars	cocktail bars	juice bars & smoothies	barbeque	japanese	pubs	sushi bars	local flavor	asian fusion	diners	steakhouses	mediterranean	wine bars	southern	cajun/creole	donuts	tacos	soup	thai	beer bar	tex-mex	greek	breweries	vietnamese	chicken shop	hot dogs	indian	bagels	comfort food	cheesesteaks	ethnic food	caribbean	middle eastern	french	soul food	buffets	gastropubs	fruits & veggies	korean	bubble tea	tapas/small plates	food stands	cupcakes	noodles	wineries	cuban	spanish	acai bowls	RestaurantsPriceRange2	WiFi	Alcohol	Smoking	BYOBCorkage	AgesAllowed	num_days_open	num_hours_open	average_income	RestaurantsDelivery	OutdoorSeating	BusinessAcceptsCreditCards	BikeParking	RestaurantsTakeOut	ByAppointmentOnly	Caters	WheelchairAccessible	RestaurantsReservations	CoatCheck	DogsAllowed	RestaurantsTableService	HasTV	HappyHour	DriveThru	BusinessAcceptsBitcoin	AcceptsInsurance	RestaurantsCounterService	dairy-free	gluten-free	vegan	kosher	halal	soy-free	vegetarian	Premium_Parking	Non_Premium_Parking	state_AZ	state_CA	state_FL	state_ID	state_LA	state_MO	state_PA	state_TN
0	1.0	0.009917	1.0	1.0	1.0	0.0	0.0	0.0	0.0	1.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	1.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	1.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.000000	1.0	0.0	0.0	0.0	0.0	1.000000	0.559524	0.180427	0.0	0.0	0.0	1.0	1.0	0.0	1.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	1.0	0.0	0.0	0.0	0.0	0.0	0.0	1.0	0.0
1	1.0	0.001058	1.0	0.0	1.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	1.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.333333	0.0	0.0	0.0	0.0	0.0	0.666667	0.238095	0.237808	0.0	0.0	1.0	1.0	1.0	0.0	0.0	1.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	1.0	0.0	0.0	0.0	0.0	0.0	0.0	1.0	0.0
2	0.0	0.000132	1.0	1.0	1.0	0.0	1.0	0.0	0.0	0.0	0.0	0.0	1.0	1.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	1.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.000000	0.0	0.0	0.0	0.0	0.0	0.833333	0.392857	0.164920	1.0	1.0	1.0	0.0	1.0	0.0	0.0	1.0	0.0	0.0	0.0	0.0	1.0	0.0	1.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	1.0

GRAPHS

A graph is a pictorial representation of a set of objects where some pairs of objects are connected by links. The interconnected objects are represented by points termed as vertices, and the links that connect the vertices are called edges. The various terms and functionalities associated with a graph is described in great detail in our tutorial here.

In this chapter we are going to see how to create a graph and add various data elements to it using a python program. Following are the basic operations we perform on graphs.

-Display graph vertices
-Display graph edges
-Add a vertex
-Add an edge
-Creating a graph

A graph can be easily presented using the python dictionary data types. We represent the vertices as the keys of the dictionary and the connection between the vertices also called edges as the values in the dictionary.

What are graph algorithms used for?

Graph algorithms are used to solve the problems of representing graphs as networks like airline flights, how the Internet is connected, or social network connectivity on Facebook. They are also popular in NLP and machine learning to form networks

**Variables Relationship (Graphs)**

Given the number of variables provided to our models, we will now graph and study the relationships between them thorugh Graphs Theory.

Despite the number of variables there are three main groups. Those comming from categories (type of food), attributes and states.

plt.figure(figsize=(15, 15))
# Creates the empty graph
G = nx.Graph()

# Add the vertices to the graph
for i, row in restaurants.iterrows():
    G.add_node(row['restaurants'])

# Add edges to the graph
for i, row in restaurants.iterrows():
    for category in row.index[5:-44]:
        if row[category] == 1:
            G.add_edge(row['restaurants'], category)

# Assign each vertex a different color
colors = ['#E6DAA6', '#F5F5DC', '#069AF3', '#13EAC9', '#90EE90', '#F5DEB3', '#C5C9C7']
node_colors = {v: colors[i % len(colors)] for i, v in enumerate(G.nodes())}

# Draw the graph with the colors assigned to each vertex.
pos = nx.fruchterman_reingold_layout(G)
nx.draw(G, pos, with_labels=True, node_color=list(map(node_colors.get, G.nodes())))

# Show the graph
plt.show()
print("The Graph has " + str(G.number_of_nodes()) + " nodes and " + str(G.number_of_edges()) + 
      " edges")

The Graph has 71 nodes and 92 edges

In the graph above we can observe the relationship between variables we had left obtained from the original column categories. We can observe two main groups, the first one is what we can called traditional restaurants with common node is the 1 for restaurants. The other group is businesses that might not be allocated as traditional restaurats as pubs, juice bars & smoothies or coffee & tea. This last group belongs for both nodes 1 and 0 for restautants.

plt.figure(figsize=(15, 15))
# Creates the empty graph
G = nx.Graph()

# Add the vertices to the graph
for i, row in restaurants.iterrows():
    G.add_node(row['restaurants'])

# Add edges to the graph
for i, row in restaurants.iterrows():
    for category in row.index[-45:-8]:
        if row[category] == 1:
            G.add_edge(row['restaurants'], category)

# Assign each vertex a different color
colors = ['#E6DAA6', '#F5F5DC', '#069AF3', '#13EAC9', '#90EE90', '#F5DEB3', '#C5C9C7']
node_colors = {v: colors[i % len(colors)] for i, v in enumerate(G.nodes())}

# Draw the graph with the colors assigned to each vertex.
nx.draw(G, with_labels=True, node_color=list(map(node_colors.get, G.nodes())))

# Show the graph
plt.show()
print("The Graph has " + str(G.number_of_nodes()) + " nodes and " + str(G.number_of_edges()) + 
      " edges")

The Graph has 38 nodes and 64 edges

Similar to the previous graph, in this one we plotted the attributes. Due to the fact that these are more ambiguous in the sense that they are more difficult to separate them in groups, the Graph stoll differenciates them depeding on the retaurants value.

plt.figure(figsize=(20, 20))

# Creates the empty graph
G = nx.Graph()

# We obtain the names of the columns
columns = restaurants.columns

# We filter the status columns
state_columns = columns[-8:]

# We filter the columns by food type
food_columns = columns[4:71]

# Iterate over the rows of the dataframe
for i, row in restaurants.iterrows():
    # We create a node for each state
    for state in state_columns:
        if row[state]:
            G.add_node(state)
    
    # We create a node for each type of food.
    for food in food_columns:
        if row[food]:
            G.add_node(food)
    
    # We add a connection between the state and the corresponding type of food.
    for state in state_columns:
        if row[state]:
            for food in food_columns:
                if row[food]:
                    G.add_edge(state, food)

# We draw the graph
nx.draw(G, with_labels=True)
print("The Graph has " + str(G.number_of_nodes()) + " nodes and " + str(G.number_of_edges()) + 
      " edges")

The Graph has 75 nodes and 536 edges

One of the most interesting things in the dataset is to know what the relationships between states and restaurant categories are. But, since the number of states and categories is so high we end up with 75 nodes and 536 edged. The amount of data, does not let us visualize the relationships. We will make a selection of representative states and categories.

plt.figure(figsize=(15, 15))
# Creates the empty graph
G = nx.Graph()

# We obtain the names of the columns
columns = restaurants.columns

# Select the status columns
state_columns = columns[columns.isin(['state_CA', 'state_TN', 'state_PA', 'state_FL', 'state_LA'])]

# We select the food type columns
food_columns = columns[columns.isin(['american (traditional)', 'american (new)', 'mexican', 'italian', 
                                     'chinese', 'japanese', 'mediterranean', 'greek', 'vietnamese', 'indian', 
                                     'caribbean', 'middle eastern', 'French', 'korean', 'cuban', 'spanish'])]

# We create a list of colors for each edge.
edge_colors = []

# Iterate over the rows of the dataframe
for i, row in restaurants.iterrows():
    # We create a node for each state
    for state in state_columns:
        if row[state]:
            G.add_node(state)
    
    # We create a node for each type of food.
    for food in food_columns:
        if row[food]:
            G.add_node(food)
    
    # We add a connection between the state and the corresponding type of food.
    for state in state_columns:
        if row[state]:
            for food in food_columns:
                if row[food]:
                    G.add_edge(state, food)
                    # We change the color of the edge depending on the state
                    if state == 'state_CA':
                        edge_colors.append('#E50000') #red                    
                    elif state == 'state_TN':
                        edge_colors.append('#DBB40C') #gold
                    elif state == 'state_PA':
                        edge_colors.append('#0343DF') #blue
                    elif state == 'state_FL':
                        edge_colors.append('#008000') #green
                    elif state == 'state_LA':
                        edge_colors.append('#F97306') #orange                      

# We draw the graph
nx.draw(G, with_labels=True, edge_color=edge_colors)
print("The Graph has " + str(G.number_of_nodes()) + " nodes and " + str(G.number_of_edges()) + 
      " edges")

The Graph has 20 nodes and 75 edges

By only selecting 5 representative states and some categories (focusing on type of cusine) we can take a better look to the relationships between cusines and states. At first glance we might look at more blue edges representing the Pennsilvania state. Recalling from the notebook "0.Data Reading and Problem statement" this state had the most amount of business, what can lead to more variety, and more relationships.

We can observe that with some exceptions, every state includes esvery typ of cusine. The exceptions are the spanish, american (traditional), korean, mediterranean and japanese with only had relations with the aforementioned Pennsilvania and Florida, another high count of business state.

One thing that seems surprising is the no relationship between mexican food and california, as the state is heavely influenced by this culture and considered one of the most multicultural.